Merging matter and geometry in the same Lagrangian

AbstractWe show that a Lagrangian density proportional to −gLm2/R reduces to a pressuron theory of gravity that is indistinguishable from General Relativity in the dust limit. The combination of matter and geometry in the same Lagrangian density intrinsically satisfies Mach's Principle — since matter cannot exist without curvature and vice versa — while it may have the correct phenomenology in order to describe actual gravity